Angular motion and impulse Draft script

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1 Introduction Many sports skills involve circular motion. Circular motion refers to the motion around a circle or curve such as spinning, turning, flipping, and twisting. Throwing the discus, hammer and shot involve angular motion. Legs and arms rotate about the joint when running, kicking and throwing. Indeed, almost every motion we do has some sort of angular or circular motion aspect to it. In this module we overview the key angular motion terminology and discuss some of the more relevant applications to an athlete's performance of a skill. Angular Displacement Quite often when we are analyzing the athlete's performance of a skill we need to understand and describe what is going on in terms the athlete's angular displacement. When an athlete is rotating free in space the rotation occurs around their center of mass. A gymnast performing a forward somersault will have a total angular displacement of 360 degrees around their center of mass in a clockwise direction. Here you see the angular displacement of the forearm around the elbow joint. Angular displacement is measured in radians, degrees or revolutions. You will see angular displacement labeled as the Greek letter theta. Every part of the forearm has the same displacement. The hand has displaced at an angle of theta, the mid forearm has displaced at an angle of theta (θ). All parts of the arm and hammer handle are being displaced by the same angle relative to to the starting point. Measuring angular displacement is useful for identifying errors. For example, here is a comparison of a runner's knee lift before and after corrective training. Here the angle the thigh makes with the center of mass is not sufficient and the foot will hit the ground moving forward causing a negative reaction force. By increasing theta the foot will hit the ground almost beneath the center of mass minimizing the deceleration effect of the foot hitting the ground because the horizontal reaction force is smaller. Angular Velocity/Speed Angular velocity is the rate of change of angular displacement. It's how fast the athlete is turning and is expressed in degrees per second, or revolutions per minute. Like linear velocity, angular velocity has magnitude and direction. Like linear speed, angular speed is just the magnitude in degrees/second direction is not an issue.

2 The equation for angular velocity is: ω = θ/t or angular velocity = angular displacement/time Now, this is an important point. The angular velocity of all parts of the body part is the same. The hammer head is moving at the same angular velocity as the throwers hands. What is different is the linear velocity here and here. Angular velocity versus Linear Velocity Circular motion converts to linear motion at the end point. The formula is V = r ω where r is the radius of the circle and ω Greek is used to indicate angular velocity. Examples include the golf swing, discus and hammer throw. All points have the same angular velocity but different linear velocities. The longer the radius the higher the linear velocity at the end of the implement. In performing many sports skills it is often best to maximize the length of the radius or lever being used and to strike the object at the end of the lever. For example, in cricket, bowlers will generate more speed on the ball if they use a straight arm. A straight arm lengthens the lever or radius of the circle through which the arm moves. In a tennis serve a fully stretched arm will ensure the racquet head is moving at its top speed at the moment of impact. However, as with most force production in many sports skills, accuracy in addition to force is important. Increasing the length of the lever too much can create handling errors. A softball player would not use a 4-meter long bat. Some players will shorten their grip on the bat or club to improve accuracy. For junior players, racquets and bats are often shortened to match the strength and height of the player. Beginners may find they do not have the strength to produce the correct technique if the racquet or bat is too long and heavy for them. Moment of inertia Now that you understand linear and angular motion we need to revisit the concept of inertia. In the linear world we defined inertia as resistance to acceleration. If the athlete wants to accelerate a force is required. To move out of the starting blocks the sprinter applies a force back against the blocks this causes them to accelerate out of the blocks. A more massive athlete will need to apply more force to move that a smaller athlete will require. That bigger athlete has more inertia. In other words the inertia of an object is directly proportional to its mass. When we start to rotate in a circle inertia also has an impact. However, we have to take another form of inertia into consideration. This is its moment of inertia or

3 rotational inertia. Here's an experiment to demonstrate the moment of inertia effect. You can do this yourself by using the weighted bar you find in most gyms. If you hold this bar in the middle it is quite easy to rotate. If you grab the bar at the end and try to spin it you will notice it is much harder. So, this is simple to remember. Rotational inertia is resistance to rotational motion. However, to understand rotational inertia we must consider how the mass is distributed. When you hold the bar in the middle the mass is equally distributed. However, when you hold the bar at the end all the mass is distributed away from the axis of rotation. Younger cricketers, baseball or softball players holding their bat further down the handle reduces the distance from the hands to the main mass of the bat and therefore reduces the bat's moment of inertia. It is easier for them to swing the bat. During running, the leg moves from the back of the body to the front (called the swing phase). The leg swings about the hip joint. The more mass that is located further from the pivot the larger the moment of inertia of the leg and the more effort it will take to accelerate the leg forward. The moment of inertia of the leg is reduced by bending the knee. This makes it easier to move forward. Kicking is another example. The kicking leg begins in the bent position. This makes it easier to generate angular velocity because the leg has a smaller moment of inertia. The knee is opened out to a straight position just before contact with the ball to increase the length of the radius, and therefore there will be a larger linear velocity. Conservation of rotational (angular) momentum Newton s first law of motion that is, the law of inertia states that an object will continue doing what it's doing unless another force is applied. A soccer ball will keep going until it is stopped by friction or another player intercepts it. Newton's first law also true for angular motion. However, you can manipulate the speed of the rotation without applying an external force. If no external force is applied and you manipulate the distribution of mass you change the moment of inertia. When the moment of inertia is reduced the speed of rotation will increase. When you increase the moment of inertia the speed of rotation slows down. The angular momentum is still the same because angular momentum = moment of inertia x angular velocity. In other words, the angular momentum is conserved. Here is a chap rotating about his center of mass. His moment of inertia is smaller here

4 than it is here. In this case his angular velocity is larger than over here. He will be spinning faster here than here. In both cases the angular momentum is the same. Here's a demonstration of the conservation of angular momentum. In sport, this concept is quite valuable to performing many skills. When spinning on the ice, skaters rotate faster by moving their limbs closer to the axis of rotation or extend their arms and legs to slow down their rotation. Divers and gymnasts also manipulate their angular velocity by changing their moment of inertia. A long jumper using the hang style is trying to lengthen their body as much as possible to slow down the forward rotation generated at take off. Impulse The only way to change an object's momentum is to apply a force. Changing momentum is an important aspect of performing many skills. Momentum is increased or decreased by varying the time over which the force is applied. The combination of force and time is referred to as impulse. In equation form: Linear impulse = Force x Time Angular impulse = Torque x Time To get the same velocity change your could have: A small force for a long time A large force for a short time A small force applied over a long period of time can be as effective as a large force applied over a short period of time. A push pass in hockey generates more momentum on the ball the longer the ball stays in contact with the stick. In track and field the athlete is usually limited to a relatively short time, so it it usually necessary to produce very high force quickly to get a large impulse and large change in momentum. A sprinter starting a race will push off the blocks and then take a series of short, fast steps to maximize the time the feet have in contact with the ground. This maximizes the momentum developed. A discus thrower uses intricate footwork in the wind-up to maximize the distance and time spent generating force. In some sports, such as softball and golf, the only way impulse can be increased is by increasing the force applied.

5 Absorbing force In addition to applying force, the human body also absorbs force. When we land from a height, the momentum of the body causes the knees, ankles and hip joints to flex. The muscles of these leg joints give during landing to cushion the impact. The same is true when catching a ball that is heavy or thrown very hard the muscles contract and give. Landing pits in track and field are designed to lengthen the time of landing to lessen the force. References Blazevich, A. Sports Biomechanics the basics. Optimising human performance Bartlett, R. Introduction to sports biomechanics. Analyzing human movement patterns Hede C, Russell K, Weatherby R. Applying biomechanics to sport. Oxford University Press, Australia.